On ℚ-Conic Bundles, III

Abstract

A ℚ-conic bundle germ is a proper morphism from a threefold with only terminal singularities to the germ (Z_∋_o) of a normal surface such that fibers are connected and the anti-canonical divisor is relatively ample. Building upon our previous paper [MP08a], we prove the existence of a Du Val anti-canonical member under the assumption that the central fiber is irreducible.